Generalized Kac-Moody algebras and the modular function \(j\)
type: Item
instance of: scholarly article
title: Generalized Kac-Moody algebras and the modular function \(j\)
zbMATH Open document ID: 0787.17022
DOI: 10.1007/BF01459740
author: Seok-Jin Kang
published in: Mathematische Annalen
publication date: 1994-05-23T00:00:00Z
full work available at URL: https://eudml.org/doc/165176
review text: We obtain a closed form root multiplicity formula for all symmetrizable generalized Kac-Moody algebras using the Weyl-Kac-Borcherds character formula and the denominator identity. Our formula enables us to study the structure of a symmetrizable generalized Kac-Moody algebra \({\mathfrak g}\) as a representation of a Kac-Moody algebra \({\mathfrak g}_ 0\) contained in \({\mathfrak g}\). Applying our formula to the Monster Lie algebra, we obtain some interesting relations for the coefficients of the elliptic modular function \(j\).
reviewed by: Seok-Jin Kang
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 11F22
zbMATH DE Number: 537322
zbMATH Keywords: root multiplicity formula
zbMATH Keywords: symmetrizable generalized Kac-Moody algebras
zbMATH Keywords: Weyl-Kac-Borcherds character formula
zbMATH Keywords: denominator identity
zbMATH Keywords: Monster Lie algebra
zbMATH Keywords: elliptic modular function
MaRDI profile type: Publication
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OpenAlex ID: W1998496313
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description: scientific article; zbMATH DE number 537322